Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity
Gen Yoneda, Hisaaki Shinkai (Waseda University)
TL;DR
This paper addresses the treatment of constraints and reality conditions in the Ashtekar formulation of general relativity, introducing a new variable to solve these conditions simultaneously in vacuum spacetimes with a cosmological constant.
Contribution
It introduces a new variable that enables simultaneous solution of gauge constraints and reality conditions in the Ashtekar formulation.
Findings
Clarifies the difference between metric and triad reality conditions.
Proposes a method to solve constraints and reality conditions together.
Provides insights into the structure of vacuum spacetimes with cosmological constant.
Abstract
We show how to treat the constraints and reality conditions in the -ADM (Ashtekar) formulation of general relativity, for the case of a vacuum spacetime with a cosmological constant. We clarify the difference between the reality conditions on the metric and on the triad. Assuming the triad reality condition, we find a new variable, allowing us to solve the gauge constraint equations and the reality conditions simultaneously.
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